The 135L vignettes at F/2 on FF. On your 550D, It doesn't see this because of the crop sensor and the 5D will show this. I believe it just the learning curve of getting used to the MK3, and how the Camera "behaves". You might have to expose more to right or stop down to remove the vignette.
Have you tried turning on peripheral illumination correction? Or added the 135L profile to the camera (Looks like it's not
). On your JPGs this can help reduce the vignetting, although it's (more or less) just boosting the edges exposure before storing it as a JPG.
With the overall dimmer images, what settings would you normally have shot on your 550D? Those should still be valid, but you are able to go up to a much higher ISO and still get pretty clean shots. You can also change around the metering modes which would affect the Auto-ISO on M which it performs. If I recall, there's some (artificial) limitations that Canon has done with Auto-ISO on M mode. With the Metering, most of the time (depends on mode) it'll take what's in the center of the image and weight that a bit more towards the determining the correct exposure. Personally, I'd go with something like 1/500, f/2-f/4, ISO 3200. That'll give you pretty good shutter speed, and if you can managed to stop down a bit to f/4 it'll give you a bit more DoF which will be useful in getting more of your subject(s) in focus. Using this calculator
, at f/2 and 20 feet, your DoF is .79 feet. Pretty shallow. If you go to f/4 you get 1.57 feet which gives you a lot more leeway.
Final words of advice, experiment! The 5d3 is a vastly different beast than your 550D, and congratulations on getting it. I know going from my 5d2 to 5d3 was a pretty large change with the somewhat different ergonomics and the vastly more complex AF system. It'll take you at least a few weeks of constant shooting in a variety of situations before you'll start getting comfortable with the AF system. Don't be afraid to experiment with the different modes and settings, it's a fantastic system and you'll get it!